Remark 4.2 
As it can be seen from Equation (REF ), the dynamics of \(s\)  have
the property that \(\dot{s} \rightarrow -k_\text{d}s\)  as \(\varepsilon \rightarrow \infty \) , implying that
the rate of integration will decrease with large cross-track errors. In particular, the
integral term will be less dominant when the cross-track error
is large, i.e., when the microswimmer is far from the desired line \(\mathcal {P}\) . As stated
in [1]}, such
error-dependent attenuation of integral action will reduce the risk of
integrator wind-up and its resulting performance limitations.

